Q1. Rationalise the denominator:
- 1/√2
- 3/√5
- 5/2√3
- 7/√7
- 4/√11
- 6/3√2
- 2/(√3 + √2)
- 5/(√7 − √3)
- 3/(2 + √5)
- 4/(3 − √2)
Q2. Convert into rational form / Simplify:
- √18 / √2
- √50 / √2
- 3√12 / √3
- √45 / √5
- 2√75 / √3
- √98 / √2
- 4√27 / √3
- √32 / √2
- √72 / √2
- 5√48 / √3
Q3. Simplify using laws of exponents:
- 2³ × 2⁵
- 5⁶ ÷ 5²
- (3²)⁴
- 10⁴ × 10³
- 7⁵ ÷ 7³
- (2³)²
- 4³ × 4²
- 9⁵ ÷ 9²
- (5²)³
- 6⁴ ÷ 6²
Q4. Solve:
- (2⁵ × 2³) ÷ 2⁴
- 5⁷ ÷ (5² × 5³)
- (3⁶ × 3²) ÷ 3⁵
- (2⁴ × 2³) ÷ 2⁵
- 10⁶ ÷ 10²
- (7³ × 7²) ÷ 7⁴
- (4⁵ ÷ 4²) × 4³
- (9⁶ ÷ 9³) × 9²
Q5. Find the value:
- 2⁵
- 10⁶
- 3⁴ × 3²
- 5⁵
- 6³
- 8²
- 7⁴
- 9³
Q6. Rationalise:
- 1/(√5 + √2)
- 4/(3 + √7)
- 6/(√3 − √2)
- 5/(√6 + √5)
- 2/(√8 − √3)
Q7. Word Problems:
- A number is written as 2⁶. Find its value.
- Find the value of 10⁵.
- Simplify 4³ × 4².
- If 3³ = 27, then find 3⁵.
- Rationalise 1/√8.
Activity Work:
- Write all laws of exponents with examples.
- Make a chart on rationalising denominator.
- Solve 10 extra sums on exponents.
- Learn squares from 1 to 30 and cubes from 1 to 15.
Happy Summer Vacation! 📚✏️